On the monotonic property of the probability of undetected errorfor a shortened code

The monotonic property of the probability of undetected error is considered when a shortened code of a linear code over GF(q) is used for error detection on a q-ary symmetric channel. Some conditions are presented under which the probability of undetected error is (or is not) monotonic with respect to the code length or the symbol error probability. It is shown that the probability of undetected error for a maximum distance separable code is monotonic with respect to the codelength. It is also shown that the probability of undetected error of a shortened code of any binary cyclic Hamming code generated by a trinomial is not monotonic with respect to the bit-error rate if the code length is short     

Suboptimum decoding of decomposable block codes

To decode a long block code with a large minimum distance by maximum likelihood decoding is practically impossible because the decoding complexity is simply enormous. However, if a code can be decomposed into constituent codes with smaller dimensions and simpler structure, it is possible to devise a practical and yet efficient scheme to decode the code. This paper investigates a class of decomposable codes, their distance and structural properties. It is shown that this class includes several classes of well-known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage (soft-decision or hard-decision) decoding scheme for decomposable codes, their translates or unions of translates is devised, and its error performance is analyzed for an AWGN channel. The two-stage soft-decision decoding is suboptimum. Error performances of some specific decomposable codes based on the proposed two-stage soft-decision decoding are evaluated. It is shown that the proposed two-stage suboptimum decoding scheme provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length     

On binary images of shortened cyclic (8, 5) codes over GF(2/sup 8/)

We have generated binary images of a large number of shortened cyclic (8, 5) codes over GF(2/sup 8/) and have computed weight distributions of the binary images of the codes. Based on the weight distributions, we have chosen four codes with the largest minimum weight 8 and the second largest minimum weight 7 among the generated codes. Over an additive white Gaussian noise channel with binary phase-shift keying modulation, simulation results have shown that block error rates of the chosen codes by a soft-decision decoding based on order-2 reprocessing are smaller than those of (64, 40) subcodes of Reed-Muller (64, 42) code by maximum likelihood decoding.     

Some decision problems related to the reachability problem for Petri nets

In this paper, we show that (1) the question to decide whether a given Petri net is consistent, M_o-reversible or live is reduced to the reachability problem in a unified manner, (2) the reachability problem for Petri nets is equivalent to the equality problem and the inclusion problem for the sets of all firing sequences of two Petri nets, (3) the equality problem for the sets of firing sequences of two Petri nets with only two unbounded places under homomorphism is undecidable, (4) the coverability and reachability problems are undecidable for generalized Petri nets in which a distinguished transition has priority over the other transitions, and (5) the reachability problem is undecidable for generalized Petri nets in which some transitions can reset a certain place to zero marking.     

On bit-error probability of a concatenated coding scheme

This paper presents a method for evaluating the bit-error probability of a concatenated coding system for BPSK transmission over the AWGN channel. In the concatenated system, a linear binary block code is used as the inner code and is decoded with the soft-decision maximum likelihood decoding, and a maximum distance separable code (or its interleaved code) is used as the outer code and is decoded with a bounded distance decoding. The method is illustrated through a specific example in which the inner code is a binary (64.40.8) Reed-Muller subcode and the outer code is the NASA standard (255, 223, 33) Reed-Solomon code over GF(2⁸) interleaved to a depth of 5. This specific concatenated system is being considered for NASA's high-speed satellite communications. The bit-error performance is evaluated by a combination of simulation and analysis. The split weight enumerators for the maximum distance separable codes are derived and used for the analysis     

A cascaded coding scheme for error control and its performanceanalysis

A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error-correcting codes, called the inner and outer codes. Its error performance is analyzed for a binary symmetric channel with a bit-error rate ϵ<1/2. It is shown that, if the inner and outer codes are chosen properly, high reliability can be attained even for a high-channel bit-error rate. Specific examples with inner codes ranging from high rates to low rates and Reed-Solomon codes as outer codes are considered, and their error probabilities evaluated. They all provide high reliability even for high bit-error rates, say 10^-1-10 ^-2. Several example schemes are being considered for such satellite and spacecraft downlink error control     

On the Probability of Undetected Error for the Maximum Distance Separable Codes

In this paper we investigate the performance of maximum-distance-separable codes with symbols fromGF(q)when they are used for pure error detection or for simultaneous error correction and detection over aq-input andq-output discret memoryless channel with symbol error probability ε. First we show that the probability of undetected error for an MDS code used for pure error detection is upper bounded byq^{-r}and decreases monotonically as εdecreases from(q - 1)/qto 0, whereris the number of parity-check symbols of the code. Then we show that the probability of undetected error for an MDS code used for correctingtor fewer symbol errors is upper bounded byq^{-r} Summin{i=0}max{t}(min{i} max{n})(q - 1)^{i}and decreases monotonically as ε decreases from(q - 1)/qto 0. These results show that the MDS codes are effective for both pure error detection and simultaneous error correction and detection.     

Development of a method for liquid xenon purification using a cryogenic centrifugal pump

We are developing a new type of photon detector for an experiment to search for muons decaying into a positron and a gamma ray. In this experiment, the photon detector will utilize liquid xenon (Xe) as the scintillation material. Good transparency of the liquid Xe is required in order to gain the highest performance out of the detector. Impurities like water and oxygen must be removed efficiently for this purpose. We have developed a new purification system, dedicated to removing water from liquid Xe, by employing a cryogenic centrifugal pump and molecular sieves. The performance of the system is described in this article.     

A Concatenated Coding Scheme for Error Control

In this paper, a concatenated coding scheme for error control in data communications is presented and analyzed. In this scheme, the inner code is used for both error correction and detection; however, the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error (or decoding error) of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughput efficiency of the proposed error control scheme incorporated with a selective-repeat ARQ retransmission strategy is also analyzed. Three specific examples are presented. One of the examples is proposed for error control in the NASA Telecommand System.